The existence of a GTT for GPTs such as quantum theory or real-vector-space
quantum theory [1]}, [2]}, [3]}, [4]}
has a number of consequences. It becomes possible, for example, to
modify the axiomatic structure of the theories as it is no longer
necessary to, separately and independently, stipulate both the
state space and the observables of the theory. Our result can
also be used to derive the standard GPT framework from operational
assumptions different to those found in the literature. More specifically,
the standard GPT framework is recovered if—after motivating the
standard description of observables in GPTs—states are assumed
to correspond to frame functions of these observables.
